CHICAGO—Florida Sen. Marco Rubio cast himself Tuesday as “a new president for a new age,” laying out a series of economic initiatives to boost growth and give lower- and middle-income Americans access to the training and education needed to gain a foothold in the 21st-century economy.

The Republican candidate outlined the proposals in an economic speech in which he urged policy makers to help workers overcome challenges presented by globalization, the technology revolution that spawned the Internet, and the automation displacing workers in all segments of the economy.

“The path to the middle class is narrower today than it has been for generations, and the American dream so many achieved in the last century is in peril,” Mr. Rubio said, at a technology hub in Chicago’s Merchandise Mart where entrepreneurs congregate to work on new ventures. “It is not the result of a cyclical economic downturn that will naturally correct itself. It is borne of a fundamental transformation.”

Mr. Rubio and several of his GOP rivals have made the economy, particularly wage stagnation and the sense that working-class Americans are falling behind, a central theme of their campaigns. Mr. Rubio is using his background as the son of a bartender and hotel maid to align himself with people who haven’t enjoyed the benefits of the economic recovery.

Some candidates and their advisers believe the eventual nominee will be the candidate who offers the best recipe to address these concerns.

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Most of the remedies Mr. Rubio proposed are staples of his economic-policy platform, including plans to reduce corporate tax rates to 25%, curb federal regulations by putting a cap on how much they cost, and allow companies to bring overseas revenue back to the U.S. without an additional tax hit. He also would cut taxes on business investments and give the public more access to the digital spectrum controlled by the federal government.

Mr. Rubio, who authored a tax plan with Sen. Mike Lee (R., Utah), would leave the top individual tax rate at 35%, unlike some of his GOP rivals. New Jersey Gov. Chris Christie’s top tax rate would be 28%. Kentucky Sen. Rand Paul has called for scrapping the current tax code and replacing it with a 14.5% flat tax on all income, regardless of how much money a person makes.

Many candidates haven't yet offered detailed plans, including former Florida Gov. Jeb Bush and former Secretary of State Hillary Clinton, the clear favorite for the Democratic nomination.

A number of prominent conservatives have criticized Mr. Rubio’s tax proposals, saying they would add to the deficit unless they were paired with other policy changes to cut federal spending. Others disagree with his calls to expand the child-tax credit, expressing doubt about whether his $2,500 credit would spur economic growth.

One cornerstone of the speech—and Mr. Rubio’s campaign—was his vow to revamp the higher-education system by expanding access to trade schools and for-profit colleges and making it easier for students to secure federally protected loans.

On Tuesday, he promised to “bust” the higher-education “cartel” dominated by “existing colleges and universities.”

The Florida senator also wants to let companies pay for employees’ education, invest more in vocational training starting in high school, and require schools to tell prospective students how much they can expect to earn after graduation, depending on the degrees they pursue.

Mr. Rubio took shots at Mrs. Clinton and made veiled swipes at Mr. Bush’s father and brother. The government shouldn’t raise taxes as it did under Presidents George H.W. Bush and Bill Clinton, he said, or “grow government” like it did under Jeb Bush’s brother, President George W. Bush.

“The race for the future will never be won by going backward,” Mr. Rubio said.

On Tuesday, Jeb Bush’s campaign unveiled a new video calling him an executive who made “tough decisions” that spurred job growth and balanced the state’s budget—a not-too-subtle contrast with Mr. Rubio and other current and former senators in the race.